Historical data indicates that only 20% of cable customers are willing to switch companies.If a binomial process is assumed,then in a sample of 20 cable customers,what is the probability that no more than 3 customers would be willing to switch their cable?
A)0.85
B)0.15
C)0.20
D)0.411
E)0.589

Question

Quizplus · Accepted Answer

This is a binomial probability problem with n=20 and p=0.2 (probability of success, which in this case is a customer willing to switch their cable). We want to find the probability that no more than 3 customers (x) would be willing to switch their cable. We can use the binomial probability formula: P(X ≤ 3) = ΣP(X = x) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

P(X = 0) = (20 choose 0) * (0.2)^0 * (0.8)^20 = 0.0115
P(X = 1) = (20 choose 1) * (0.2)^1 * (0.8)^19 = 0.0746
P(X = 2) = (20 choose 2) * (0.2)^2 * (0.8)^18 = 0.2023
P(X = 3) = (20 choose 3) * (0.2)^3 * (0.8)^17 = 0.3024

Adding these probabilities, we get P(X ≤ 3) = 0.0115 + 0.0746 + 0.2023 + 0.3024 = 0.411. Therefore, the answer is D.

Historical Data Indicates That Only 20% of Cable Customers Are